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### Pipe Expansion Thermal Loop Equations and Calculator

Fluids and Flow Design and Engineering

Pipe Thermal Expansion U Shape Loop Equations and Calculator for Pipe

Thermal expansion will occur between all fixed points in a piping system. If the system has the same covering height, natural fixed points will occur in the center of a line section between two expansion elbows. Unequal covering will cause the fixed point to be displaced due to varying frictional forces, and if there is any doubt, the fixed point should be set with an anchor. In all cases, this fixed point should be considered when calculating requirments for a pipe expansion loop.

Δ L = c · L · ( Tf - Ta )

Loop Length

(W + 2H ) = [ ( 3 · E · D · Δ L ) / S ) ]1/2

Where:

ΔL = Thermal Expansion of known pipe length between fixed anchor points (in, mm),
c = Coefficient of expansion ( in/in °F, mm/mm °C ),
L = Distance between fixed anchor points (in, mm) ,
Tf = Temperature of fluid ( °F, °C ),
Ta = Temperature ambient (ground) to pipe ( °F, °C )
D = Diameter Outside of pipe (in, mm)
W = Width length of pipe (in, mm)
H = Height length of pipe (in, mm)
E = Modulus of elasticity (lb/in2, kPa)
S = Allowable stress in pipe (lb/in2, kPa)

* Keep units consistant (first units, second units)

Design Guidelines For Pipe Expansion Loop.

• The expansion loop is usually located on the side of the hottest line.
• The expansion loop, as a rule, should be located in the center of the distance between two anchors.
• The height of the expansion loop is normally twice the width. The exception to this rule occurs when more than one line runs parallel in a common trench. The dimensions of the loops for the additional line must be increased to allow nesting of the loops.
 — — — — Temp. Thermal Expansion of Pipe Inches per 100 ft. mm per 100 meters °F Carbon Steel Copper Stainless Steel °C –40 –0.288 –0.421 –0.461 –40 –24,0 –35,1 –38,4 –20 –0.145 –0.210 – 0.230 –28 –12,1 –17,4 –19,0 0 0 0 0 –17 0 0 0 20 0.148 0.238 0.230 –6 12,5 19,7 19,0 32 0.230 0.366 0.369 0 19,0 30,5 30,8 40 0.300 0.451 0.461 4 24,9 37,7 38,4 60 0.448 0.684 0.691 15 37,4 57,1 57,7 80 0.580 0.896 0.922 26 48,2 74,8 76,8 100 0.753 1.134 1.152 37 62,7 94,5 96,1 120 0.910 1.366 1.382 48 75,8 113,9 115,2 140 1.064 1.590 1.613 60 88,6 132,6 134,5 160 1.200 1.804 1.843 71 100,1 150,3 153,6 180 1.360 2.051 2.074 82 113,2 170,9 172,9 200 1.520 2.296 2.304 93 126,6 191,3 191,9 212 1.610 2.428 2.442 100 134,2 202,4 203,4 220 1.680 2.516 2.534 104 140,1 209,7 211,3 230 1.760 2.636 2.650 110 146,7 219,8 220,8 260 2.020 126 168,3 280 2.180 137 181,8 300 2.350 148 195,9 320 2.530 160 211,0 340 2.700 171 225,1 350 2.790 176 232,6